This paper proposes two separable approaches for analyzing reliability of fault-tolerant systems that are possibly subject to both common-cause failures (CCF) and imperfect fault coverage (IPC). Almost all the existing reliability assessment methods either fail to consider CCF or fail to consider IPC. Both cases result in exaggerated system reliability. Our methods provide accurate reliability by incorporating both CCF and IPC into the reliability modeling for an arbitrary system. Further, the two methods have low computational complexity in that they separate the consideration of both IPC and CCF from the combinatorics of the solution. The methods are illustrated with a concrete analysis of a sample network system. A general illustration of those approaches in the context of two important classes of reliability problems: networks and fault trees, is also provided.